Aguilo, IsabelRiera, Juan VicenteSuner, JaumeTorrens, Joan2024-09-132024-09-132020-12Aguilo I, Vicente Riera J, Suner J, Torrens J. Modus tollens with respect to uninorms: U-Modus Tollens. Int J Approx Reasoning. 2020 Dec;127:54-69.0888-613Xhttp://hdl.handle.net/20.500.13003/17230https://hdl.handle.net/20.500.12105/22902In fuzzy logic and approximate reasoning the inference rule given by the Modus Tollens usually derives into an inequality involving three logical operators: a conjunction, an implication function and a negation. Until now, in this scenario the conjunction has been commonly modeled by a t-norm, but recently the possibility of using a more general conjunction has been pointed out. In this work, we want to generalize the Modus Tollens inequality by using a conjunctive uninorm instead of a t-norm, leading to the so-called U-Modus Tollens. First, we give a study of this new property for implication functions in general and then we specially focus on residual implications derived from uninorms. In all cases, we prove that there are a lot of solutions of the U-Modus Tollens and we give a characterization of all the solutions in some particular cases. (c) 2020 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).enghttp://creativecommons.org/licenses/by-nc-nd/4.0/Modus TollensUninormImplication functionRU-implicationresearch articleAttribution-NonCommercial-NoDerivatives 4.0 International12754-6910.1016/j.ijar.2020.10.0031873-4731International Journal of Approximate Reasoningopen access2-s2.0-85093646670591502900004